Fractional order PI controllers for TCP packet flow ensuring given modulus margins
|
|
- Abner Hamilton
- 6 years ago
- Views:
Transcription
1 Control and Cybernetics vol. 43 (2014) No. 4 Fractional order PI controllers for TCP packet flow ensuring given modulus margins by Wies law Krajewski 1 and Umberto Viaro 2 1 Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, Warsaw, Poland krajewsk@ibspan.waw.pl 2 Department of Electrical Management and Mechanical Engineering, University of Udine, via delle Scienze 206, Udine, Italy viaro@uniud.it Abstract: An Active Queue Management (AQM) robust control strategy for Traffic Control Protocol (TCP) data transfer is proposed. To this purpose, the TCP behaviour is first approximated by a second order model with delayed input obtained from the linearization of an efficient and commonly used nonlinear fluid based model. The adopted feedback control structure uses a fractional order PI controller. To ensure the desired robustness, the parameter regions where such a controller guarantees a given modulus margin (inverse of the H norm of the sensitivity function) are derived. An example commonly used in the literature is worked out to show that the suggested graphically based design technique is simple to apply while it limits the effects of disturbances and of the unmodelled dynamics. Keywords: fractional-order PI controllers, robust control, TCP congestion control, delayed systems 1. Introduction Transmission Control Protocol(TCP) is one of the core protocols of the internet protocol suite(forouzan, 2010). It is used by about 90% of the Internet Protocol (IP) traffic in the Internet. The IP task is to exchange pieces of information called datagrams. Due to network congestion, traffic load balancing, or other unpredictable causes, IP packets can be lost or delivered out of order. TCP Submitted: August 2014; Accepted: November 2014 This paper has been presented in its original version at the conference BOS 2014 (Operational and Systems Research) in Warsaw, in September 2014.
2 494 W. Krajewski and U. Viaro detects these situations, requests retransmission of lost packets, rearranges out of order packets, and then passes the restored data to the application program, thus separating the application s communication from networking details. Network congestion depends on the limitation of all network resources, such as router processing time and link throughput. To avoid, at least in part, this problem, core routers mark, or even drop, TCP packets with the objective of managing network utilization and queuing delay. This task is called Active Queue Management (AQM) (Low, Paganini and Doyle, 2002; Chatranon, Labrador and Banerjee, 2004). Various AQM algorithms have been proposed and applied, from the first Random Early Detection (RED) (Floyd and Jacobson, 1993; Hollot et al., 2001) method to the more robust and reliable Proportional plus Integral (PI) control that can be run with its default parameters in most circumstances. To enable the application to AQM of the control engineering principles, such as the PI scheme, a suitable dynamic model of the TCP behaviour is required. An effective TCP model has been developed in Misra, Gong and Towsley (2000) and adopted in Hollot et al. (2002) to tune the parameters of P and PI controllers. A similar model for wireless networks has also been used in Yanping (2011). Simulations using the network simulator ns-2 have confirmed the usefulness of such a control engineering approach. The two main sources of difficulties in the analysis of TCP dynamics are the input and state delay, on the one hand, and the parameter uncertainties and variations, on the other. To deal with the control of uncertain time delayed systems in a proper way, different approaches have been proposed recently. Particularly interesting in this regard is the geometrical method described in Klamka and Tańcula (2010, 2012a,b), where the set of uncertain parameter values ensuring either asymptotic stability or D-stability has been determined with reference to the popular Random Early Detection (RED) algorithm for queue management (modelled as a first order transfer function in the feedback control channel). Noninteger order systems have been considered with increasing interest in the recent control literature, because many plants can be described more satisfactorily by models of this kind (Chen, Petráš and Xue, 2009; Petráš, 2009) or because noninteger order controllers provide a better performance than the classic integer order ones (Podlubny, 1999). In fact, it has been shown that in many instances the fractional order PID controllers outperform the best integer order PID controllers (Luo and Chen, 2009; Chao et al., 2009). In the following, we consider the situation in which queue management is carried out using a fractional order PI controller and the controlled system is described by a second order model plus a time delay obtained from the nonlinear model derived in Misra, Gong and Towsley (2000). A similar approach has recently been followed with reference to wireless networks in Yanping (2011) using classic frequency domain specifications. Robustness is a fundamental issue in AQM and in noninteger order control, too (see. e.g., Quet and Ozbay, 2004). In particular, it is very important to de-
3 Fractional order PI controllers for TCP packet flow ensuring given modulus margins 495 termine the set of PI λ controllers that satisfy certain stability margins. Among these margins, the modulus margin (also called H margin because it is the inverse of the H norm of the sensitivity function) seems to be the most meaningful (Garcia, Karimi and Longchamp, 2004; Krajewski, Lepschy and Viaro, 2004). Determining the controllers that ensure a given modulus margin, however, is not an easy task even for integer order systems. Such problem has been tackled, e.g., in Krajewski and Viaro (2012) for integer order time-delay plants and PID controllers using different approaches. Here, we extend the essentially graphic method from Krajewski and Viaro (2012) to the aforementioned case of PI λ controllers. The entire stability region in the space of controller parameters has already been determined in Hamamci (2007), Ruszewski (2008), and, for particular classes of fractional order controllers and time delay plants, in Hamamci and Koksal (2010), Rahimian and Tavazoei (2010), where, however, no indication is given regarding the loci of the constant modulus margin. The remainder of this paper is organized as follows. In Section 2, the aforementioned TCP fluid based model is briefly recalled. The considered control problem is stated in Section 3. The equation of the stability boundary in the controller parameter plane is derived in Section 4 along the lines followed in Krajewski and Viaro (2012) for the integer order case. The loci of constant modulus margin are determined in Section 5 and plotted using a dedicated Matlab problem. An example frequently considered in the literature shows the effectiveness of the adopted approach in Section 6. A few concluding remarks are made in Section TCP flow model By ignoring the TCP timeout mechanism, the nonlinear dynamic model of TCP behaviour developed in Misra, Gong and Towsley (2000) is described by the following pair of nonlinear differential equations: 1 Ẇ(t) = R(t) W(t)W(t R(t)) p (t R(t)) 2R(t R(t)) (1) q(t) = W(t) N(t) C R(t) (2) where: W = expected TCP window size in packets, q = expected queue length in packets, R = q C +T p = round trip time in seconds, C = link capacity in packets per second, T p = propagation delay in seconds, N = number of TCP sessions (load factor), p = probability of packet marking or dropping. The window size W and the queue length q are non negative and bounded, that is, W [0,W max ], q [0,q max ], where W max and q max denote the maximum
4 496 W. Krajewski and U. Viaro window size and buffer capacity, respectively. Obviously, p [0, 1]. The number N of sessions and the link capacity C are assumed constant. The above model has a unique equilibrium point (W 0,q 0,p 0 ), characterized by W 0 = R 0C N, W2 0p 0 = 2, R 0 = q 0 C +T p. (3) By linearizing equations (1) (2) about this point and taking into account the considerations from Hollot et al. (2001), the model becomes δw(t) = 2N R 0C 2 R0 2CδW(t) 2N 2 δp(t R 0), (4) δq(t) = N R 0 δw(t) 1 R 0 δq(t), (5) where δw(t). = W(t) W 0, δq(t). = q(t) q 0, and δp(t). = p(t) p 0. The deviations δw(t) and δq(t) represent the state variables, whereas δp(t) is the control variable. The main task of the AQM algorithm is to relate the queue length q at the bottleneck router to the marking probability p, and then inform the TCP sender on the state of congestion. For the adopted model the transfer function between δp(t) and δq(t) turns out to be: G(s) = C2 2N e sr 0 (s+ 2N 1, (6) R0 2C)(s+ ) R 0 so that the TCP behaviour is locally described by a linear second order model with delayed input and poles at 2N/(R 2 0 C) and 1/R 0. Clearly, the control signal δp(t) should drive the state [δw(t), δq(t)] T of the linearized model to the origin. The main goals of the control system design are: (i) to ensure suitable stability margins, (ii) to allow for efficient queueing utilization, and (iii) to guarantee robustness against uncertainties and disturbances. 3. Problem statement Consider a unity feedback control system and assume that the controlled plant is described by the transfer function: G(s) = n(s) d(s) e Ts, (7) where: n(s) = C2 2N, d(s) = s2 +( 2N R0 2C + 1 )s + 2N R 0 R 3 C, and T = R 0 is a time delay.
5 Fractional order PI controllers for TCP packet flow ensuring given modulus margins 497 Assume also that plant is controlled by means of a standard PI λ controller described by the transfer function: C(s) = k p + k i sλ, (8) where λ > 0, and k p, k i are the proportional and integral gain, respectively. Clearly, this setting encompasses any combination of integer order time delay plant and integer order or noninteger order controller. The problem we refer to is that of finding a controller as in equation (8) in such a way that the overall unity feedback control system is stable with a modulus margin greater than a prescribed value. In the usual case of integer order controllers, there are two design parameters, i.e., k p and k i, whereas the aforementioned control problem allows for one more design parameter, i.e., λ, and this greater flexibility can be exploited in order to achieve a better performance. 4. Stability regions The Nyquist diagram of the loop function: L(s) = C(s)G(s) (9) crosses the unit circle centred at the origin with a phase equal to m ϕ π, where m ϕ is the phase margin, if: L(jω a ) = e j(mϕ π), (10) where ω a denotes the gain crossover frequency and j denotes the imaginary unit. Taking into account equations(7) and(8), the interpolation condition, expressed by equation (10), can be written as [ kp (jω a ) λ +k i ] n(jωa ) = d(jω a )(jω a ) λ e j(tωa+mϕ π). (11) Bydecomposingn(jω a )andd(jω a ) intotheirrealandimaginarypartsaccording to n(jω a ) = n r (ω a )+jn i (ω a ), d(jω a ) = d r (ω a )+jd i (ω a ), (12) equation (11) can be split into two equations relating the real and imaginary parts on both of its sides, leading, after some algebra, to k p sinλ π ( 2 = A(ω a) sin ω a T+m ϕ +λ π ) ( +B(ω a ) cos ω a T+m ϕ +λ π ), (13) 2 2 k i sinλ π [ 2 = ωλ a A(ω a ) sin ( ) ω a T +m ϕ B(ωa ) cos ( ) ] ω a T +m ϕ (14) with A(ω a ) = d r(ω a )n r (ω a )+d i (ω a )n i (ω a ) n 2 r (ω a)+n 2 r (ω a), (15) B(ω a ) = d r(ω a )n i (jω a ) d i (jω a )n r (ω a ) n 2 r (ω a)+n 2 i (ω, (16) a)
6 498 W. Krajewski and U. Viaro which provide the parametric equations (with parameter ω a ) of a curve in the (k p,k i ) plane. When m ϕ = 0, at each point of these curves 1+L(jω a ) = 0, i.e., the characteristic equation 1 + L(s) = 0 of the feedback control system exhibits the purely imaginary roots ±jω a. Therefore, on the parameter plane (k p,k i ), these curves separate regions characterized by different numbers of right half plane (RHP) and left half plane (LHP) roots of the system characteristic equation, and some of these regions may correspond to a stable behaviour. This property was proved in Krajewski and Viaro (2012) for integer order systems and controllers. For λ = 1 (integer order PI controller) equations (13) and (14) simplify to ) ) k p = A(ω a ) cos (ω a T +m ϕ B(ω a ) sin (ω a T +m ϕ, (17) k i = ω a [A(ω a ) sin ( ω a T +m ϕ ) B(ωa ) cos ( ω a T +m ϕ ) ], (18) which of course coincide with equations (10) and (11) in Krajewski and Viaro (2012). The stability boundaries have been determined for the sample network considered in Hollot et al. (2002), where C = 3750 packets/s (15Mbps), N = 60 and R 0 = s. In particular, Fig. 1 shows the stability regions for λ = 0.8, 1.0, 1.1, By way of example, the loci described by equations (13) and (14) inside the stability region for different values of the phase margin m ϕ when λ = 1.25, are shown in Fig Loci of constant modulus margin An indicator of system robustness that is more adequate than the phase and gain margins is the modulus margin defined as: δ := min ω 1+L(jω) (19) which represents the minimal distance of the Nyquist diagram of the loop function from the critical point 1 + j0 and corresponds to the reciprocal of the infinity norm of the sensitivity function. Now, the locus of the parameter points where δ = const is the envelope of the loci: 1+L(jω) = δ, ω, (20) which is equivalent to L(jω)+L(jω)+ L(jω) 2 = δ 2 1, (21) where the overbar denotes complex conjugate.
7 Fractional order PI controllers for TCP packet flow ensuring given modulus margins 499 Figure 1. Stability regions for different values of the exponent λ in equation (8) (regions below the curves, corresponding to each value of λ, and above the horizontal axis) when the plant transfer function is given by equation (6), with C = 3750 packets/s (15Mbps), N = 60 and R 0 = s Simple algebra leads from equation (21) to ( kp ω λ) 2 +k 2 i +2k i ( kp ω λ) cosλ π 2 +2k pω 2λ[ A(ω)cosωT +B(ω)sinωT] +2k i ω λ[ A(ω)cos(ωT +λ π 2 )+B(ω)sin(ωT +λπ 2 ) ] = ω 2λ d2 r(ω)+d 2 i (ω) n 2 r(ω)+n 2 i (ω)(δ2 1), (22) which is the equation of an ellipse in the (k p,k i ) plane, whose centre can be found using standard procedures of analytic geometry. The region, where δ > 0.2 inside the stability area for the plant model in equation (6) with C = 3750 packets/s, N = 60, R 0 = 0.246, and λ = 1.25 in equation (8), is shown in Fig. 3: it is given by the area under the lower envelope of the family of ellipses. 6. Example In Hollot et al. (2002), to control the considered plant, the integer order PI controller C(s) = k p + ki s with k p = and k i = has been adopted. It locally stabilizes the equilibrium point corresponding to the
8 500 W. Krajewski and U. Viaro Figure 2. Loci described by equations (13) and (14) for λ = 1.25 and phase margin m ϕ = 0, π 8, π 4, π 3, when the plant transfer function is given by equation (6) with C = 3750 packets/s (15Mbps), N = 60 and R 0 = s parameter values that characterize the nominal plant, i.e., C = 3750 packets/s, N = 60 and R 0 = However, this PI controller is rather fragile since the point (k p,k i ) = ( , ) is close to the stability boundary (see the point P 1 in Fig. 4). A less fragile controller is obtained for k p = and k i = (corresponding to the point P 2 in Fig. 4) which ensure almost the same behaviour of the feedback control system as the controller proposed in Hollot et al. (2002), when the plant parameter take the nominal values. Fig. 5 shows the unit step responses of the control system with this less fragile controller for the nominal plant with C = 3750 packets/s, N = 60, R 0 = 0.246, as well as for the two partly perturbed plant models with C = 3750 packets/s, N = 80, R 0 = 0.15 and, respectively, C = 3750 packets/s, N = 45, R 0 = 0.4. In the last case the considered PI controller (and, to a greater extent, the less robust controller derived in Hollot et al., 2002) does not even guarantee stability. Fig. 6depictsthestepresponsesforthesameplantmodelswhenafractional order PI λ controller, characterized by the same values of k p and k i, and by λ = 1.25, is adopted. The control system performance is better than that afforded by the integer order controller. In particular, the fractional order controller locally stabilizes the system in all of the three cases, thus ensuring greater robustness.
9 Fractional order PI controllers for TCP packet flow ensuring given modulus margins 501 Figure 3. Family of ellipses corresponding to ω (0.2,5.0) rad/s when δ = 0.2 and λ = 1.25 in equation (22). The lower envelope of this family delimits the area of the first two quadrants, where stability is ensured, and the modulus margin satisfies the inequality δ > Conclusions A fractional orderpi λ controllerhas been applied to the controlof TCP packet flows. The regions of the controller parameter space, where given stability margins are ensured, have been determined. Particular attention has been given to the so called modulus margin that accounts well for system robustness. The loci of constant stability margins in the parameter space have been plotted using a simple Matlab program. As shown in Section 6, these curves can profitably be used to design robust fractional order controllers in a simple and intuitive way. It is believed that considerable improvements over conventional AQM techniques can be achieved in terms of both performance and robustness using fractional order controllers in conjunction with modulus margin specifications. References Chao, H., Luo, Y., Di, L., and Chen, Y.Q. (2009) Fractional order flight control of a small fixed wing UAV: Controller design and simulation study. In: Proc. ASME 2009 Int. Design Engineering Tech. Conferences and
10 502 W. Krajewski and U. Viaro Figure 4. A part of the area where stability is ensured and the modulus margin satisfies the inequality δ > 0.2. The point P 1 = (k p,k i ) = ( , ) corresponds to the PI controller derived in Hollot et al. (2002), whereas the point P 2 = (k p,k i ) = ( , ) corresponds to a less fragile controller ensuring almost the same dynamic behaviour for the nominal plant Computers and Information in Engineering Conference, San Diego, CA, USA, Aug. 30 Sept. 2, 2009, ASME, Chatranon, G., Labrador, M.A., and Banerjee, S. (2004) A survey of TCP friendly router based AQM schemes. Computer Communications, 27, 15, Elsevier, Chen, Y.K., Petráš, I., and Xue, D. (2009) Fractional order control - A tutorial. In: Proceedings of American Control Conference, St. Louis, MI, USA, June 10 12, 2009, IEEE Inc., Floyd, S. and Jacobson, V. (1993) Random early detection gateways for congestion avoidance. IEEE/ACM Trans. Networking, 1, 4, IEEE Press, Forouzan, B.A. (2010) TCP/IP Protocol Suite. McGraw-Hill Higher Education, Boston, MA, USA (4th edition). Garcia, D., Karimi, A., and Longchamp, R.(2004) Robust PID controller tuning with specification on modulus margin. In: Proc. American Control Conf., Boston,MA,USA,4, June30 July2, IEEEInc., Hamamci, S. E. (2007) An algorithm for stabilization of fractional order time delay systems using fractio-nal order PID controllers. IEEE Trans. Automat. Contr., 52, 10,
11 Fractional order PI controllers for TCP packet flow ensuring given modulus margins 503 Figure 5. Step responses for the integer order PI controller with k p = and k i = (point P 2 in Fig. 4) when the plant parameters are: (i) C = 3750 packets/s, N = 60, R 0 = (solid line), (ii) C = 3750 packets/s, N = 80, R 0 = 0.15 (dotted line), and (iii) C = 3750 packets/s, N = 45, R 0 = 0.4 (dashed line) Hamamci, S. E. and Koksal, M. (2010) Calculation of all stabilizing fractional order PD controllers for integrating time delay systems. In: Computers and Mathematics with Applications, 59, 5, Hollot, C.V., Misra, V., Towsley, D., and Gong, W.B. (2001) A control theoretic analysis of RED. In: Proc. IEEE INFOCOM, Anchorage, AK, USA, April IEEE, 3, Hollot, C.V., Misra, V., Towsley, D., and Gong, W.B. (2002) Analysis and design of controllers for AQM routers supporting TCP flows. IEEE Trans. Automat. Contr., 47, 6, Klamka, J. and Tańcula, J. (2010) Examination of robust stability of computer networks. In: Proc. 6-th Int. Working Conf. Performance Modeling and Evaluation of Heterogeneous Networks, Zakopane, Poland, Jan , 2010, Inst. Theoretical and Appl. Informatics, Pol. Acad. Sci., Klamka, J. and Tańcula, J. (2012a) Analiza D-stabilności protoko lu TCP- DCR. Studia Informatica, 33, 3A (107), Klamka, J. and Tańcula, J. (2012b) Examination of robust D-stability of TCP-DCR. Theoretical and Applied Informatics, 24, 4, Krajewski, W., Lepschy, A. and Viaro, U. (2004) Designing PI controllers for robust stability and performance. IEEE Trans. Control Syst.
12 504 W. Krajewski and U. Viaro Figure 6. Step responses afforded by the fractional order PI controller with k p = , k i = and λ = 1.25 when the plant parameters are: (i) C = 3750 packets/s, N = 60, R 0 = (nominal plant, solid line), (ii) C = 3750 packets/s, N = 80, R 0 = 0.15 (dotted line), and (iii) C = 3750 packets/s, N = 45, R 0 = 0.4 (dashed line) Technol., 12, 6, Krajewski, W., Lepschy, A., Miani, S. and Viaro, U.(2005) Frequency domain approach to robust PI control. J. Franklin Inst., 342, 6, Krajewski, W. and Viaro, U. (2012) On robust PID control for time delay plants. In: Proc.17th IEEE Int. Conf. Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, Aug , IEEE, Low, S.H., Paganini, F. and Doyle, J.C. (2002) Internet congestion control. IEEE Contr. Syst. Mag., 22, 1, Luo, Y. and Chen, Y.Q. (2009) Fractional order [proportional derivative] controller for a class of fractional order systems. Automatica, 45, 10, Misra, V., Gong, W.B., and Towsley, D. (2000) Fluid based analysis of a network of AQM routers supporting TCP flows with an application to RED. In: Proc. ACM/SIGCOMM, Stockholm, Sweden, Aug. 28 Sept. 1. ACM Press, Petráš, I. (2009) Stability of fractional order systems with rational orders: A survey. Fract. Calc. Appl. Anal., 12, 3, Podlubny, I. (1999) Fractional order systems andpi λ D µ controllers. IEEE Trans. Automat. Contr., 44, 1,
13 Fractional order PI controllers for TCP packet flow ensuring given modulus margins 505 Quet, P.F. and Özbay, H. (2002) On the design of AQM supporting TCP flows using robust control theory. IEEE Trans. Automat. Contr., 49, 6, Rahimian, M. A. and Tavazoei, M. S. (2010) Stabilizing fractional order PI and PD controllers: An integer order implemented system approach. Proc. of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 224, 8, Ruszewski, A. (2008) Stability regions of closed loop system with time delay inertial plant of fractional order and fractional order PI controller. Bull. Polish Acad. Sciences, Tech. Sciences, 56, 4, Yanping, Q., Wenkui, H., Xiangze, L., and Bing, W. (2011) Fractional order proportional integral controller for active queue management of wireless network. In: Proc. Chinese Control Conference, Yantai, China, July 22 24, IEEE,
Hopf Bifurcation and Stability of an Improved Fluid Flow Model with Time Delay in Internet Congestion Control
International Journal of Engineering esearch And Management (IJEM) ISSN: 349-58, Volume-5, Issue-6, June 18 Hopf Bifurcation and Stability of an Improved Fluid Flow Model with Time Delay in Internet Congestion
More informationAnalysis and Design of Controllers for AQM Routers Supporting TCP Flows
To appear in IEEE TAC s special issue on Systems and Control Methods for Communication Networks Analysis and Design of Controllers for AQM Routers Supporting TCP Flows C.V. Hollot, V. Misra, D. Towsley
More informationRobust PID and Fractional PI Controllers Tuning for General Plant Model
2 مجلة البصرة للعلوم الهندسية-المجلد 5 العدد 25 Robust PID and Fractional PI Controllers Tuning for General Plant Model Dr. Basil H. Jasim. Department of electrical Engineering University of Basrah College
More informationOSCILLATION AND PERIOD DOUBLING IN TCP/RED SYSTEM: ANALYSIS AND VERIFICATION
International Journal of Bifurcation and Chaos, Vol. 18, No. 5 (28) 1459 1475 c World Scientific Publishing Company OSCILLATION AND PERIOD DOUBLING IN TCP/RED SYSTEM: ANALYSIS AND VERIFICATION XI CHEN,
More informationRobust Loop Shaping Controller Design for Spectral Models by Quadratic Programming
Robust Loop Shaping Controller Design for Spectral Models by Quadratic Programming Gorka Galdos, Alireza Karimi and Roland Longchamp Abstract A quadratic programming approach is proposed to tune fixed-order
More informationModeling and Stability of PERT
Modeling Stability of PET Yueping Zhang yueping@cs.tamu.edu I. SYSTEM MODEL Our modeling of PET is composed of three parts: window adjustment ED emulation queuing behavior. We start with the window dynamics.
More informationComplete Stability Region Characterization for PI-AQM
Complete Stability Region Characterization for PI-AQM Ahmad T. Al-Hammouri, Vincenzo Liberatore, Michael S. ranicky Department of Electrical Engineering and Computer Science Case Western Reserve University
More informationRobust Stability Analysis of a class of Smith Predictor-based Congestion Control algorithms for Computer Networks
Robust Stability Analysis of a class of Smith Predictor-based Congestion Control algorithms for Computer Networs Luca De Cicco, Saverio Mascolo and Silviu I. Niculescu Abstract Congestion control is a
More informationFEL3210 Multivariable Feedback Control
FEL3210 Multivariable Feedback Control Lecture 5: Uncertainty and Robustness in SISO Systems [Ch.7-(8)] Elling W. Jacobsen, Automatic Control Lab, KTH Lecture 5:Uncertainty and Robustness () FEL3210 MIMO
More informationActive queue management with discrete sliding modes in TCP networks
BULLETIN OF THE POLISH ACADEMY OF SCIENCES TECHNICAL SCIENCES, Vol. 62, No. 4, 214 DOI: 1.2478/bpasts-214-76 INFORMATICS Active queue management with discrete sliding modes in TCP networks P. IGNACIUK
More informationNetwork anomaly estimation for TCP/AQM networks using an observer
1 Network anomaly estimation for TCP/AQM networks using an observer Yassine Ariba, Yann Labit, Frederic Gouaisbaut University of Toulouse, LAAS-CNRS 7 avenue du Colonel Roche, 3177 Toulouse cedex 4 FRANCE
More informationCongestion Control for Infrastructure-based CRNs: A Multiple Model Predictive Control Approach
Congestion Control for Infrastructure-based CRNs: A Multiple Model Predictive Control Approach Kefan Xiao, Shiwen Mao, and Jitendra K Tugnait Department of Electrical and Computer Engineering, Auburn University,
More informationResearch Article Design of the Congestion Control for TCP/AQM Network with Time-Delay
Mathematical Problems in Engineering, Article ID 834698, 7 pages http://dx.doi.org/.55/4/834698 Research Article Design of the Congestion Control for TCP/AQM Network with Time-Delay Dazhong Wang and Shujing
More informationInternet Congestion Control: Equilibrium and Dynamics
Internet Congestion Control: Equilibrium and Dynamics A. Kevin Tang Cornell University ISS Seminar, Princeton University, February 21, 2008 Networks and Corresponding Theories Power networks (Maxwell Theory)
More informationA New TCP/AQM System Analysis
A ew TCP/AQM System Analysis Qin Xu, Fan Li, Jinsheng Sun, and Moshe Zukerman, Fellow, IEEE arxiv:37.24v [cs.i] 4 Jul 23 Abstract The fluid model has been used extensively to guide designs of AQM schemes
More informationRobust fixed-order H Controller Design for Spectral Models by Convex Optimization
Robust fixed-order H Controller Design for Spectral Models by Convex Optimization Alireza Karimi, Gorka Galdos and Roland Longchamp Abstract A new approach for robust fixed-order H controller design by
More informationIntroduction. Performance and Robustness (Chapter 1) Advanced Control Systems Spring / 31
Introduction Classical Control Robust Control u(t) y(t) G u(t) G + y(t) G : nominal model G = G + : plant uncertainty Uncertainty sources : Structured : parametric uncertainty, multimodel uncertainty Unstructured
More informationBoundedness of AIMD/RED System with Time Delays
Boundedness of AIMD/ED System with Time Delays Lijun Wang 1, Lin Cai, Xinzhi Liu 1 and Xuemin (Sherman) Shen 3 Department of Applied Mathematics 1, Department of Electrical and Computer Engineering 3 University
More informationDesign and Tuning of Fractional-order PID Controllers for Time-delayed Processes
Design and Tuning of Fractional-order PID Controllers for Time-delayed Processes Emmanuel Edet Technology and Innovation Centre University of Strathclyde 99 George Street Glasgow, United Kingdom emmanuel.edet@strath.ac.uk
More informationLecture 6. Chapter 8: Robust Stability and Performance Analysis for MIMO Systems. Eugenio Schuster.
Lecture 6 Chapter 8: Robust Stability and Performance Analysis for MIMO Systems Eugenio Schuster schuster@lehigh.edu Mechanical Engineering and Mechanics Lehigh University Lecture 6 p. 1/73 6.1 General
More information384Y Project June 5, Stability of Congestion Control Algorithms Using Control Theory with an application to XCP
384Y Project June 5, 00 Stability of Congestion Control Algorithms Using Control Theory with an application to XCP . Introduction During recent years, a lot of work has been done towards the theoretical
More informationStability Analysis of TCP/RED Communication Algorithms
Stability Analysis of TCP/RED Communication Algorithms Ljiljana Trajković Simon Fraser University, Vancouver, Canada ljilja@cs.sfu.ca http://www.ensc.sfu.ca/~ljilja Collaborators Mingjian Liu and Hui Zhang
More informationControlo Switched Systems: Mixing Logic with Differential Equations. João P. Hespanha. University of California at Santa Barbara.
Controlo 00 5 th Portuguese Conference on Automatic Control University of Aveiro,, September 5-7, 5 00 Switched Systems: Mixing Logic with Differential Equations João P. Hespanha University of California
More informationRobust Tuning of Power System Stabilizers Using Coefficient Diagram Method
International Journal of Electrical Engineering. ISSN 0974-2158 Volume 7, Number 2 (2014), pp. 257-270 International Research Publication House http://www.irphouse.com Robust Tuning of Power System Stabilizers
More informationSwitched Systems: Mixing Logic with Differential Equations
research supported by NSF Switched Systems: Mixing Logic with Differential Equations João P. Hespanha Center for Control Dynamical Systems and Computation Outline Logic-based switched systems framework
More informationROBUST CONGESTION CONTROL OF TCP/IP FLOWS. Computer Control Laboratory,Groupe ESIEE, 2 Bld. Blaise Pascal, Noisy Le Grand, France
ROBUST CONGESTION CONTROL OF TCP/IP FLOWS A.CELA C.IONETE M. BEN GAID Computer Control Laboratory,Groupe ESIEE, 2 Bld. Blaise Pascal, 9362 Noisy Le Grand, France Abstract: The growth in the TCP/IP traffic
More informationStability Analysis of TCP/RED Communication Algorithms
Stability Analysis of TCP/RED Communication Algorithms Ljiljana Trajković Simon Fraser University, Vancouver, Canada ljilja@cs.sfu.ca http://www.ensc.sfu.ca/~ljilja Collaborators Mingjian Liu and Hui Zhang
More informationA NEW APPROACH TO MIXED H 2 /H OPTIMAL PI/PID CONTROLLER DESIGN
Copyright 2002 IFAC 15th Triennial World Congress, Barcelona, Spain A NEW APPROACH TO MIXED H 2 /H OPTIMAL PI/PID CONTROLLER DESIGN Chyi Hwang,1 Chun-Yen Hsiao Department of Chemical Engineering National
More informationSingular perturbation analysis of an additive increase multiplicative decrease control algorithm under time-varying buffering delays.
Singular perturbation analysis of an additive increase multiplicative decrease control algorithm under time-varying buffering delays. V. Guffens 1 and G. Bastin 2 Intelligent Systems and Networks Research
More informationClassify a transfer function to see which order or ramp it can follow and with which expected error.
Dr. J. Tani, Prof. Dr. E. Frazzoli 5-059-00 Control Systems I (Autumn 208) Exercise Set 0 Topic: Specifications for Feedback Systems Discussion: 30.. 208 Learning objectives: The student can grizzi@ethz.ch,
More informationAutomatic Control 2. Loop shaping. Prof. Alberto Bemporad. University of Trento. Academic year
Automatic Control 2 Loop shaping Prof. Alberto Bemporad University of Trento Academic year 21-211 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 21-211 1 / 39 Feedback
More informationControl Systems I. Lecture 9: The Nyquist condition
Control Systems I Lecture 9: The Nyquist condition Readings: Åstrom and Murray, Chapter 9.1 4 www.cds.caltech.edu/~murray/amwiki/index.php/first_edition Jacopo Tani Institute for Dynamic Systems and Control
More informationRobustness of Real and Virtual Queue based Active Queue Management Schemes
Robustness of Real and Virtual Queue based Active Queue Management Schemes Ashvin Lakshmikantha, C. L. Beck and R. Srikant Department of General Engineering University of Illinois lkshmknt@uiuc.edu, rsrikant@uiuc.edu,
More informationFrequency methods for the analysis of feedback systems. Lecture 6. Loop analysis of feedback systems. Nyquist approach to study stability
Lecture 6. Loop analysis of feedback systems 1. Motivation 2. Graphical representation of frequency response: Bode and Nyquist curves 3. Nyquist stability theorem 4. Stability margins Frequency methods
More informationPM diagram of the Transfer Function and its use in the Design of Controllers
PM diagram of the Transfer Function and its use in the Design of Controllers Santiago Garrido, Luis Moreno Abstract This paper presents the graphical chromatic representation of the phase and the magnitude
More informationFragility via Robustness of Controllers Dedicated. to the Congestion Control in Internet Protocol
Applied Mathematical Sciences, Vol. 7, 2013, no. 88, 4353-4362 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2013.3528 Fragility via Robustness of Controllers Dedicated to the Congestion
More informationRobust and Gain-Scheduled PID Controller Design for Condensing Boilers by Linear Programming
Robust and Gain-Scheduled PID Controller Design for Condensing Boilers by Linear Programming Vinicius de Oliveira and Alireza Karimi Laboratoire d Automatque École Polytechnique Fédérale de Lausanne (EPFL)
More informationThe loop shaping paradigm. Lecture 7. Loop analysis of feedback systems (2) Essential specifications (2)
Lecture 7. Loop analysis of feedback systems (2). Loop shaping 2. Performance limitations The loop shaping paradigm. Estimate performance and robustness of the feedback system from the loop transfer L(jω)
More informationIterative Controller Tuning Using Bode s Integrals
Iterative Controller Tuning Using Bode s Integrals A. Karimi, D. Garcia and R. Longchamp Laboratoire d automatique, École Polytechnique Fédérale de Lausanne (EPFL), 05 Lausanne, Switzerland. email: alireza.karimi@epfl.ch
More informationON MAIN CHARACTERISTICS OF THE M/M/1/N QUEUE WITH SINGLE AND BATCH ARRIVALS AND THE QUEUE SIZE CONTROLLED BY AQM ALGORITHMS
K Y B E R N E T I K A V O L U M E 4 7 ( 2 0 1 1 ), N U M B E R 6, P A G E S 9 3 0 9 4 3 ON MAIN CHARACTERISTICS OF THE M/M/1/N QUEUE WITH SINGLE AND BATCH ARRIVALS AND THE QUEUE SIZE CONTROLLED BY AQM
More informationTopic # Feedback Control Systems
Topic #19 16.31 Feedback Control Systems Stengel Chapter 6 Question: how well do the large gain and phase margins discussed for LQR map over to DOFB using LQR and LQE (called LQG)? Fall 2010 16.30/31 19
More informationControl Systems I. Lecture 9: The Nyquist condition
Control Systems I Lecture 9: The Nyquist condition adings: Guzzella, Chapter 9.4 6 Åstrom and Murray, Chapter 9.1 4 www.cds.caltech.edu/~murray/amwiki/index.php/first_edition Emilio Frazzoli Institute
More informationAnalysis of SISO Control Loops
Chapter 5 Analysis of SISO Control Loops Topics to be covered For a given controller and plant connected in feedback we ask and answer the following questions: Is the loop stable? What are the sensitivities
More informationCHAPTER 5 ROBUSTNESS ANALYSIS OF THE CONTROLLER
114 CHAPTER 5 ROBUSTNESS ANALYSIS OF THE CONTROLLER 5.1 INTRODUCTION Robust control is a branch of control theory that explicitly deals with uncertainty in its approach to controller design. It also refers
More informationFairness comparison of FAST TCP and TCP Vegas
Fairness comparison of FAST TCP and TCP Vegas Lachlan L. H. Andrew, Liansheng Tan, Tony Cui, and Moshe Zukerman ARC Special Research Centre for Ultra-Broadband Information Networks (CUBIN), an affiliated
More informationarxiv: v1 [cs.ni] 5 Feb 2009
On Designing Lyapunov-Krasovskii Based AQM for Routers Supporting TCP Flows Yann Labit, Yassine Ariba and Frédéric Gouaisbaut arxiv:0902.0922v1 [cs.ni] 5 Feb 2009 December 2007 Abstract For the last few
More informationOn Stabilization of First-Order Plus Dead-Time Unstable Processes Using PID Controllers
On Stabilization of First-Order Plus Dead-Time Unstable Processes Using PID Controllers Chyi Hwang Department of Chemical Engineering National Chung Cheng University Chia-Yi 621, TAIWAN E-mail: chmch@ccu.edu.tw
More informationUncertainty and Robustness for SISO Systems
Uncertainty and Robustness for SISO Systems ELEC 571L Robust Multivariable Control prepared by: Greg Stewart Outline Nature of uncertainty (models and signals). Physical sources of model uncertainty. Mathematical
More informationLecture 1: Feedback Control Loop
Lecture : Feedback Control Loop Loop Transfer function The standard feedback control system structure is depicted in Figure. This represend(t) n(t) r(t) e(t) u(t) v(t) η(t) y(t) F (s) C(s) P (s) Figure
More informationChapter 2. Classical Control System Design. Dutch Institute of Systems and Control
Chapter 2 Classical Control System Design Overview Ch. 2. 2. Classical control system design Introduction Introduction Steady-state Steady-state errors errors Type Type k k systems systems Integral Integral
More informationPIQI-RCP: Design and Analysis of Rate-Based Explicit Congestion Control
PIQI-RCP: Design and Analysis of Rate-Based Explicit Congestion Control Saurabh Jain Joint work with Dr. Dmitri Loguinov June 21, 2007 1 Agenda Introduction Analysis of RCP QI-RCP PIQI-RCP Comparison Wrap
More informationNew Results in Generalized Minimum Variance Control of Computer Networks
ISSN 1392 124X (print), ISSN 2335 884X (online) INFORMATION TECHNOLOGY AND CONTROL, 2014, T. 43, Nr. 3 New Results in Generalized Minimum Variance Control of Computer Networks Wojciech Przemysław Hunek
More informationQuantitative Feedback Theory based Controller Design of an Unstable System
Quantitative Feedback Theory based Controller Design of an Unstable System Chandrima Roy Department of E.C.E, Assistant Professor Heritage Institute of Technology, Kolkata, WB Kalyankumar Datta Department
More information7.4 STEP BY STEP PROCEDURE TO DRAW THE ROOT LOCUS DIAGRAM
ROOT LOCUS TECHNIQUE. Values of on the root loci The value of at any point s on the root loci is determined from the following equation G( s) H( s) Product of lengths of vectors from poles of G( s)h( s)
More informationMULTILOOP PI CONTROLLER FOR ACHIEVING SIMULTANEOUS TIME AND FREQUENCY DOMAIN SPECIFICATIONS
Journal of Engineering Science and Technology Vol. 1, No. 8 (215) 113-1115 School of Engineering, Taylor s University MULTILOOP PI CONTROLLER FOR ACHIEVING SIMULTANEOUS TIME AND FREQUENCY DOMAIN SPECIFICATIONS
More informationThe Generalized Nyquist Criterion and Robustness Margins with Applications
51st IEEE Conference on Decision and Control December 10-13, 2012. Maui, Hawaii, USA The Generalized Nyquist Criterion and Robustness Margins with Applications Abbas Emami-Naeini and Robert L. Kosut Abstract
More informationACK-Clocking Dynamics: Modelling the Interaction between Windows and the Network
ACK-Clocking Dynamics: Modelling the Interaction between Windows and the Network Krister Jacobsson, Lachlan L. H. Andrew,AoTang, Karl H. Johansson,Håkan Hjalmarsson,StevenH.Low ACCESS Linnaeus Centre,
More informationResearch Article Stabilizing of Subspaces Based on DPGA and Chaos Genetic Algorithm for Optimizing State Feedback Controller
Mathematical Problems in Engineering Volume 2012, Article ID 186481, 9 pages doi:10.1155/2012/186481 Research Article Stabilizing of Subspaces Based on DPGA and Chaos Genetic Algorithm for Optimizing State
More informationTWO- PHASE APPROACH TO DESIGN ROBUST CONTROLLER FOR UNCERTAIN INTERVAL SYSTEM USING GENETIC ALGORITHM
International Journal of Electrical and Electronics Engineering Research (IJEEER) ISSN:2250-155X Vol.2, Issue 2 June 2012 27-38 TJPRC Pvt. Ltd., TWO- PHASE APPROACH TO DESIGN ROBUST CONTROLLER FOR UNCERTAIN
More informationRobust Fractional Control An overview of the research activity carried on at the University of Brescia
Università degli Studi di Brescia Dipartimento di Ingegneria dell Informazione Robust Fractional Control An overview of the research activity carried on at the University of Brescia Fabrizio Padula and
More informationDESIGN USING TRANSFORMATION TECHNIQUE CLASSICAL METHOD
206 Spring Semester ELEC733 Digital Control System LECTURE 7: DESIGN USING TRANSFORMATION TECHNIQUE CLASSICAL METHOD For a unit ramp input Tz Ez ( ) 2 ( z ) D( z) G( z) Tz e( ) lim( z) z 2 ( z ) D( z)
More informationROBUST STABILITY ANALYSIS OF SIMPLE CONTROL ALGORITHMS IN COMMUNICATION NETWORKS
ROBUST STABILITY ANALYSIS OF SIMPLE CONTROL ALGORITHMS IN COMMUNICATION NETWORKS Qing-Chang Zhong Dept of Electrical & Electronic Engineering Imperial College London Exhibition Rd, London SW7 BT United
More informationTCP over Cognitive Radio Channels
1/43 TCP over Cognitive Radio Channels Sudheer Poojary Department of ECE, Indian Institute of Science, Bangalore IEEE-IISc I-YES seminar 19 May 2016 2/43 Acknowledgments The work presented here was done
More informationQFT Framework for Robust Tuning of Power System Stabilizers
45-E-PSS-75 QFT Framework for Robust Tuning of Power System Stabilizers Seyyed Mohammad Mahdi Alavi, Roozbeh Izadi-Zamanabadi Department of Control Engineering, Aalborg University, Denmark Correspondence
More informationControl Systems I Lecture 10: System Specifications
Control Systems I Lecture 10: System Specifications Readings: Guzzella, Chapter 10 Emilio Frazzoli Institute for Dynamic Systems and Control D-MAVT ETH Zürich November 24, 2017 E. Frazzoli (ETH) Lecture
More informationRobust QFT-based PI controller for a feedforward control scheme
Integral-Derivative Control, Ghent, Belgium, May 9-11, 218 ThAT4.4 Robust QFT-based PI controller for a feedforward control scheme Ángeles Hoyo José Carlos Moreno José Luis Guzmán Tore Hägglund Dep. of
More informationAlireza Mousavi Brunel University
Alireza Mousavi Brunel University 1 » Control Process» Control Systems Design & Analysis 2 Open-Loop Control: Is normally a simple switch on and switch off process, for example a light in a room is switched
More informationA New TCP End-to-End Congestion Avoidance Algorithm Through Output Feedback
2004 5th Asian Control Conference A New TCP End-to-End Congestion Avoidance Algorithm Through Output Feedback Yi Guo*, Zhihua &U* and Nageswara bot * Department of Electrical and Computer Engineering University
More informationModelling an Isolated Compound TCP Connection
Modelling an Isolated Compound TCP Connection Alberto Blanc and Denis Collange Orange Labs 905 rue Albert Einstein Sophia Antipolis, France {Email: alberto.blanc,denis.collange}@orange-ftgroup.com Konstantin
More informationPart II. Advanced PID Design Methods
Part II Advanced PID Design Methods 54 Controller transfer function C(s) = k p (1 + 1 T i s + T d s) (71) Many extensions known to the basic design methods introduced in RT I. Four advanced approaches
More informationQFT design for uncertain non-minimum phase and unstable plants revisited
Loughborough University Institutional Repository QFT design for uncertain non-minimum phase and unstable plants revisited This item was submitted to Loughborough University's Institutional Repository by
More informationcs/ee/ids 143 Communication Networks
cs/ee/ids 143 Communication Networks Chapter 4 Transport Text: Walrand & Parakh, 2010 Steven Low CMS, EE, Caltech Agenda Internetworking n Routing across LANs, layer2-layer3 n DHCP n NAT Transport layer
More informationA Generalized FAST TCP Scheme
A Generalized FAST TCP Scheme Cao Yuan a, Liansheng Tan a,b, Lachlan L. H. Andrew c, Wei Zhang a, Moshe Zukerman d,, a Department of Computer Science, Central China Normal University, Wuhan 430079, P.R.
More informationRichiami di Controlli Automatici
Richiami di Controlli Automatici Gianmaria De Tommasi 1 1 Università degli Studi di Napoli Federico II detommas@unina.it Ottobre 2012 Corsi AnsaldoBreda G. De Tommasi (UNINA) Richiami di Controlli Automatici
More informationRobust Control. 2nd class. Spring, 2018 Instructor: Prof. Masayuki Fujita (S5-303B) Tue., 17th April, 2018, 10:45~12:15, S423 Lecture Room
Robust Control Spring, 2018 Instructor: Prof. Masayuki Fujita (S5-303B) 2nd class Tue., 17th April, 2018, 10:45~12:15, S423 Lecture Room 2. Nominal Performance 2.1 Weighted Sensitivity [SP05, Sec. 2.8,
More informationThM06-2. Coprime Factor Based Closed-Loop Model Validation Applied to a Flexible Structure
Proceedings of the 42nd IEEE Conference on Decision and Control Maui, Hawaii USA, December 2003 ThM06-2 Coprime Factor Based Closed-Loop Model Validation Applied to a Flexible Structure Marianne Crowder
More informationMAE143a: Signals & Systems (& Control) Final Exam (2011) solutions
MAE143a: Signals & Systems (& Control) Final Exam (2011) solutions Question 1. SIGNALS: Design of a noise-cancelling headphone system. 1a. Based on the low-pass filter given, design a high-pass filter,
More informationDerivation of Robust Stability Ranges for Disconnected Region with Multiple Parameters
SICE Journal of Control, Measurement, and System Integration, Vol. 10, No. 1, pp. 03 038, January 017 Derivation of Robust Stability Ranges for Disconnected Region with Multiple Parameters Tadasuke MATSUDA
More informationcommunication networks
Positive matrices associated with synchronised communication networks Abraham Berman Department of Mathematics Robert Shorten Hamilton Institute Douglas Leith Hamilton Instiute The Technion NUI Maynooth
More informationCHAPTER # 9 ROOT LOCUS ANALYSES
F K א CHAPTER # 9 ROOT LOCUS ANALYSES 1. Introduction The basic characteristic of the transient response of a closed-loop system is closely related to the location of the closed-loop poles. If the system
More informationModelling TCP with a Discrete Time Markov Chain
Modelling TCP with a Discrete Time Markov Chain José L Gil Motorola josegil@motorola.com ABSTRACT TCP is the most widely used transport protocol in the Internet. The end-to-end performance of most Internet
More informationModel-based PID tuning for high-order processes: when to approximate
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 25 Seville, Spain, December 2-5, 25 ThB5. Model-based PID tuning for high-order processes: when to approximate
More informationA Novel Integral-Based Event Triggering Control for Linear Time-Invariant Systems
53rd IEEE Conference on Decision and Control December 15-17, 2014. Los Angeles, California, USA A Novel Integral-Based Event Triggering Control for Linear Time-Invariant Systems Seyed Hossein Mousavi 1,
More informationQUANTITATIVE L P STABILITY ANALYSIS OF A CLASS OF LINEAR TIME-VARYING FEEDBACK SYSTEMS
Int. J. Appl. Math. Comput. Sci., 2003, Vol. 13, No. 2, 179 184 QUANTITATIVE L P STABILITY ANALYSIS OF A CLASS OF LINEAR TIME-VARYING FEEDBACK SYSTEMS PINI GURFIL Department of Mechanical and Aerospace
More informationQueue level Time [s]
KYBERNETIKA VOLUME 37 (21), NUMBER 3, PAGES 355 { 365 STATISTICAL{LEARNING CONTROL OF MULTIPLE{DELAY SYSTEMS WITH APPLICATIONS TO ATM NETWORKS C. T. Abdallah 1, M. Ariola 2 and V. Koltchinskii 3 Congestion
More informationReliable Data Transport: Sliding Windows
Reliable Data Transport: Sliding Windows 6.02 Fall 2013 Lecture 23 Exclusive! A Brief History of the Internet guest lecture by Prof. Hari Balakrishnan Wenesday December 4, 2013, usual 6.02 lecture time
More informationLecture 6 Classical Control Overview IV. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore
Lecture 6 Classical Control Overview IV Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore Lead Lag Compensator Design Dr. Radhakant Padhi Asst.
More informationECE 345 / ME 380 Introduction to Control Systems Lecture Notes 8
Learning Objectives ECE 345 / ME 380 Introduction to Control Systems Lecture Notes 8 Dr. Oishi oishi@unm.edu November 2, 203 State the phase and gain properties of a root locus Sketch a root locus, by
More informationData Based Design of 3Term Controllers. Data Based Design of 3 Term Controllers p. 1/10
Data Based Design of 3Term Controllers Data Based Design of 3 Term Controllers p. 1/10 Data Based Design of 3 Term Controllers p. 2/10 History Classical Control - single controller (PID, lead/lag) is designed
More informationLMI Based Model Order Reduction Considering the Minimum Phase Characteristic of the System
LMI Based Model Order Reduction Considering the Minimum Phase Characteristic of the System Gholamreza Khademi, Haniyeh Mohammadi, and Maryam Dehghani School of Electrical and Computer Engineering Shiraz
More informationECE 486 Control Systems
ECE 486 Control Systems Spring 208 Midterm #2 Information Issued: April 5, 208 Updated: April 8, 208 ˆ This document is an info sheet about the second exam of ECE 486, Spring 208. ˆ Please read the following
More informationModule 3F2: Systems and Control EXAMPLES PAPER 2 ROOT-LOCUS. Solutions
Cambridge University Engineering Dept. Third Year Module 3F: Systems and Control EXAMPLES PAPER ROOT-LOCUS Solutions. (a) For the system L(s) = (s + a)(s + b) (a, b both real) show that the root-locus
More informationStability of interval positive continuous-time linear systems
BULLETIN OF THE POLISH ACADEMY OF SCIENCES TECHNICAL SCIENCES, Vol. 66, No. 1, 2018 DOI: 10.24425/119056 Stability of interval positive continuous-time linear systems T. KACZOREK Białystok University of
More informationDr Ian R. Manchester Dr Ian R. Manchester AMME 3500 : Root Locus
Week Content Notes 1 Introduction 2 Frequency Domain Modelling 3 Transient Performance and the s-plane 4 Block Diagrams 5 Feedback System Characteristics Assign 1 Due 6 Root Locus 7 Root Locus 2 Assign
More informationPID control of FOPDT plants with dominant dead time based on the modulus optimum criterion
Archives of Control Sciences Volume 6LXII, 016 No. 1, pages 5 17 PID control of FOPDT plants with dominant dead time based on the modulus optimum criterion JAN CVEJN The modulus optimum MO criterion can
More informationRobust Control of Heterogeneous Networks (e.g. congestion control for the Internet)
Robust Control of Heterogeneous Networks (e.g. congestion control for the Internet) Glenn Vinnicombe gv@eng.cam.ac.uk. University of Cambridge & Caltech 1/29 Introduction Is it possible to build (locally
More informationIMC based automatic tuning method for PID controllers in a Smith predictor configuration
Computers and Chemical Engineering 28 (2004) 281 290 IMC based automatic tuning method for PID controllers in a Smith predictor configuration Ibrahim Kaya Department of Electrical and Electronics Engineering,
More informationLyapunov Stability of Linear Predictor Feedback for Distributed Input Delays
IEEE TRANSACTIONS ON AUTOMATIC CONTROL VOL. 56 NO. 3 MARCH 2011 655 Lyapunov Stability of Linear Predictor Feedback for Distributed Input Delays Nikolaos Bekiaris-Liberis Miroslav Krstic In this case system
More informationSimulation Study on Pressure Control using Nonlinear Input/Output Linearization Method and Classical PID Approach
Simulation Study on Pressure Control using Nonlinear Input/Output Linearization Method and Classical PID Approach Ufuk Bakirdogen*, Matthias Liermann** *Institute for Fluid Power Drives and Controls (IFAS),
More informationAircraft Stability & Control
Aircraft Stability & Control Textbook Automatic control of Aircraft and missiles 2 nd Edition by John H Blakelock References Aircraft Dynamics and Automatic Control - McRuler & Ashkenas Aerodynamics, Aeronautics
More information